Calc Tricks
If you are looking at a graph on your TI-84 and want to see the exact coordinate pairs in a data table, which two keys do you press?
What is: 2nd --> GRAPH (which opens the TABLE ).
To enter data lists (L1 and L2) to create a scatter plot or calculate a regression line, which main button do you start with?
What is: The STAT button (then select 1:Edit...).
If a multiple-choice question asks you to find the solution set to an equation like x^2 - 2x - 8 = 0, what is the fastest way to use the given answer choices to your advantage?
What is: Plug the given choices back into the equation for x (or look at y = x^2 - 2x - 8 in your calculator's table) to see which one makes the equation equal 0.
If a constructed-response question asks you to "graph the function," what must you include alongside your drawn line or curve to ensure you get full credit for your points?
What are: Clearly labeled table of data points on your exam booklet/or on the graph, and arrowheads/labels on your graphed lines.
What do we call a value or a number that makes an expression equal to zero—essentially, where the graph crosses the x-axis?
A zero, root, or x-intercept.
What is the fastest shortcut menu sequence on a TI-84 Plus to create a stacked fraction template (n/d)?
What is: ALPHA --> Y= (this opens the FRAC menu), then press ENTER on 1:n/d.
What variable on your calculator output screen represents the correlation coefficient, and what is its maximum possible perfect positive value?
What is: The variable is r, and its maximum perfect value is 1.
A question asks which function has the greatest y-intercept, giving you one equation, one graph, one table, and a verbal description. What is the safest strategy to compare them uniformly?
What is: Find the value of each when x is 0
What mathematically tragic mistake happens when a student forgets to write y = when asked to write an equation for a line?
What is: Forgetting "y =" creates an expression rather than an equation, resulting in an automatic loss of credit.
In the expression 5x2 - 4x + 7, what is the specific mathematical term for the number 5, and what is the term for the number 7?
5 is the coefficient (specifically the leading coefficient); 7 is the constant.
What is the exact step-by-step sequence of button presses required to clear out old lines and graph a brand new equation like y = -2x + 6?
What is: Press Y=, press CLEAR to empty any old equations, type (-) 2 X + 6, and then press the GRAPH button.
If your calculator gives you a linear regression output of a = 2.5, b = -4, and r = -0.92, write the actual equation for the line of best fit.
What is: y = 2.5x - 4
Many Regents questions ask you to identify an equivalent expression to something complex like (2x - 3)^2. How can you use the Y= menu to guarantee you pick the correct choice?
Type the original expression into Y1 and the answer choices into Y2, Y3, etc. Check the table (2nd --> GRAPH); the correct choice will have the exact same output values as Y1.
If a multi-part long answer question asks you to "state" or "determine" an answer, do you need to show your algebraic work? What if it says "justify" or "algebraically solve"?
For "state" or "determine," you only need the final answer (though work is safe). For "justify" or "algebraically solve," you must show step-by-step mathematical work or you will lose points even with the right answer.
Define the difference between the Domain and the Range of a function.
Domain is the set of all possible input values (x-values); Range is the set of all possible output values (y-values).
When looking at a parabola on your graph screen, you need to find the vertex. After pressing 2nd --> TRACE (CALC), what are the two possible options you must choose between depending on whether the parabola opens up or down?
What is: 3:minimum (if the parabola opens up like a U) or 4:maximum (if the parabola opens down like an upside-down U).
Explain what (positive/negative) and strength (strong/weak) describing a correlation coefficient.
Strong = close to 1 (dots close together)
Weak = farther from 1 ( dots spread out)
Negative = downward slope
Positive = upward slope
If a word problem asks for a realistic domain for "the number of people attending a theater performance," which numbers should you automatically eliminate from the choices?
What are: Negative numbers and fractions/decimals (people must be represented by whole numbers/non-negative integers).
When graphing a system of inequalities on a grid, what two final visual elements must be perfectly clear to the grader to earn full marks?
1. Line style (dashed lines for less than or greater than; solid lines for less than or equal too or greater than or equal too). 2. A big, clearly labeled "S" in the overlapping shaded region of solutions.
What is the specific term for the highest or lowest point on a parabola, and what is the name of the vertical line that splits that parabola perfectly in half?
The point is the vertex, and the line is the axis of symmetry (written as an equation in the form x = h).
You have graphed a system of equations in Y1 and Y2. To find the exact coordinate point where the two lines cross, you navigate to 2nd --> TRACE. Which option do you select, and how many times do you press ENTER to bypass the calculator's prompts?
What is: Select 5:intersect, and then press ENTER three times.
What is the equation for the line of best fit?
What is: y = ax + b
You have narrowed a difficult question down to two choices, but you are completely stuck. According to scoring rules, how much penalty do you receive for a wrong multiple-choice answer on the Algebra Regents, and what should you do?
What is: There is no penalty for guessing. You should never leave a multiple-choice question blank!
A student solves a word problem perfectly but writes down 7.432 centimeters. The question explicitly stated: "Round to the nearest tenth of a centimeter." How many points will the student lose for this rounding error?
They will lose 1 point (usually a 2-point question is reduced to 1 point for a rounding or units error). Always re-read the final sentence before moving on!
What is the mathematical definition of a rational number, and give an example of an irrational number often found on the Regents exam.
A rational number is any number that can be expressed as a fraction of two integers (a/b). An irrational number cannot.